论文标题
基于确定性的伴随半分析算法，用于快速响应变化质子治疗的计算
A deterministic adjoint-based semi-analytical algorithm for fast response change computations in proton therapy
论文作者
论文摘要
在本文中，我们提出了一种解决方案，以便在在线自适应质子治疗中需要快速粒子传输算法，但由于系统参数的变化而准确地计算出患者剂量指标的变化。我们通过数值溶液到一维fokker-Planck方程以及Fermi-Eyges方程的分析解决方案来获得质子相空间密度。此外，为伴随通量得出并解决了相应的伴随系统。质子相空间密度与伴随通量和度量（将光束沉积在可变区域中的能量选择）允许评估我们算法对系统参数和利益区域中不同扰动范围的准确性。算法可忽略不计（$ 1.1 \ times 10^{ - 6} $ $ \％$至$ 3.6 \ $ 3.6 \ times 10^{ - 3} $ $ \％$）用于小扰动范围（$ -40 \ text {$ \％$} $） - 符合伴随方法的众所周知的局限性 - 对于大型临床兴趣区域，对于大量临床利益而言，大型扰动范围（$ -400 \ text {hu to} 400 \ text {hu} $）围绕着Bragg Peak。鉴于这些结果结合了进一步提高正时性能的能力，因此可以得出结论，我们的算法为在线自适应质子疗法的特定目的提供了可行的解决方案。
In this paper we propose a solution to the need for a fast particle transport algorithm in Online Adaptive Proton Therapy capable of cheaply, but accurately computing the changes in patient dose metrics as a result of changes in the system parameters. We obtain the proton phase-space density through the product of the numerical solution to the one-dimensional Fokker-Planck equation and the analytical solution to the Fermi-Eyges equation. Moreover, a corresponding adjoint system was derived and solved for the adjoint flux. The proton phase-space density together with the adjoint flux and the metric (chosen as the energy deposited by the beam in a variable region of interest) allowed assessing the accuracy of our algorithm to different perturbation ranges in the system parameters and regions of interest. The algorithm achieved negligible errors ($1.1 \times 10^{-6}$ $\%$ to $3.6 \times 10^{-3}$ $\%$) for small perturbation ranges ($-40 \text{ HU to } 40 \text{ HU}$) and small to moderate errors ($3 \text{ $\%$ to } 17 \text{ $\%$}$) -- in line with the well-known limitation of adjoint approaches -- for large perturbation ranges ($-400 \text{ HU to } 400 \text{ HU}$) in the case of most clinical interest where the region of interest surrounds the Bragg peak. Given these results coupled with the capability of further improving the timing performance it can be concluded that our algorithm presents a viable solution for the specific purpose of Online Adaptive Proton Therapy.
